Question

По прямой дороге в одном направлении с постоянной скоростью едут на велосипедах Аня и Борис.Скорость Ани 125 м/мин,а Бориса 285 м/мин.В момент старта Аня опережала Борю на 2080 м. а)Через какое время Боря догонит Аню? б)На коком расстоянии друг от друга они будут через 15 минут после старта?

Answer 1

Ответ во вложении. Решение очевидное.

Answer 2

Problem Analysis

We have two cyclists, Anya and Boris, traveling in the same direction on a straight road. Anya's speed is 125 m/min, and Boris's speed is 285 m/min. Anya initially leads Boris by 2080 m. We need to find out two things: a) How long will it take for Boris to catch up to Anya? b) How far apart will they be after 15 minutes from the start?

Solution

Let's solve the problem step by step.

a) To find out how long it will take for Boris to catch up to Anya, we can set up an equation based on their relative speeds and the initial distance between them.

Let's assume t is the time it takes for Boris to catch up to Anya.

The distance Anya travels in time t is given by: Distance_Anya = Anya's speed * t

The distance Boris travels in time t is given by: Distance_Boris = Boris's speed * t

Since Anya initially leads Boris by 2080 m, we can set up the equation: Distance_Boris - Distance_Anya = 2080

Substituting the values, we get: (Boris's speed * t) - (Anya's speed * t) = 2080

Simplifying the equation, we get: (285 * t) - (125 * t) = 2080

Solving for t, we get: 160t = 2080

Dividing both sides by 160, we get: t = 2080 / 160

Calculating the value, we find: t ≈ 13 minutes

Therefore, it will take Boris approximately 13 minutes to catch up to Anya.

b) To find out how far apart they will be after 15 minutes from the start, we can use the same equation Distance_Boris - Distance_Anya = 2080.

Substituting the values, we get: (Boris's speed * 15) - (Anya's speed * 15) = 2080

Simplifying the equation, we get: (285 * 15) - (125 * 15) = 2080

Calculating the value, we find: 4275 - 1875 = 2400

Therefore, after 15 minutes from the start, Anya and Boris will be approximately 2400 meters apart.

Answer

a) Boris will catch up to Anya in approximately 13 minutes. b) After 15 minutes from the start, Anya and Boris will be approximately 2400 meters apart.

Please let me know if there's anything else I can help you with!